The package is used for statistical analysis of Plant Breeding experiments.
Package Website https://nandp1.github.io/gpbStat/
Note: In the latest version 0.3.1 estimation of Kings Variance is not included.
Install latest package from Github through
Install gpbStat from CRAN with:
Line by Tester analysis (only crosses).
# Loading the gpbStat package
library(gpbStat)
# Loading dataset
data(rcbdltc)
## Now by using function ltc we analyze the data.
## The first parameter of `ltc` function is "data" followed by replication, line, tester and dependent variable(yield)
results1 = ltc(rcbdltc, replication, line, tester, yield)
#>
#> Analysis of Line x Tester: yield
## Viewing the results
results1
#> $Means
#> Testers
#> Lines 6 7 8
#> 1 68.550 107.640 52.640
#> 2 73.265 97.640 85.650
#> 3 100.885 111.540 117.735
#> 4 105.795 64.450 46.855
#> 5 84.150 81.935 94.820
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 148.436 49.47866 0.509612 6.778194e-01
#> Crosses 14 26199.654 1871.40388 19.274772 6.737492e-14
#> Lines 4 10318.361 2579.59035 27.466791 1.421271e-11
#> Testers 2 1718.926 859.46289 9.151332 4.626865e-04
#> Lines X Testers 8 14162.367 1770.29589 18.849639 4.973396e-12
#> Error 42 4077.815 97.09084 NA NA
#> Total 59 30425.906 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 11.42608
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 455.48131 552.57215 97.09084
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 27.2585365 24.7481829
#> Environmental coefficient of Variation <NA>
#> 11.4260778 0.8242929
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 10318.361 2579.59035 27.466791 1.421271e-11
#> Testers 2 1718.926 859.46289 9.151332 4.626865e-04
#> Lines X Testers 8 14162.367 1770.29589 18.849639 4.973396e-12
#> Error 42 4077.815 97.09084 NA NA
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> -9.960 -0.718 23.817 -13.870 0.732
#>
#> $`GCA testers`
#> 6 7 8
#> 0.292 6.404 -6.697
#>
#> $`SCA crosses`
#> Testers
#> Lines 6 7 8
#> 1 -8.019 24.959 -16.940
#> 2 -12.546 5.717 6.828
#> 3 -9.461 -4.918 14.378
#> 4 33.136 -14.321 -18.815
#> 5 -3.111 -11.438 14.548
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 39.383578 6.560872 54.055550
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> 67.441205 -45.541650
#> Cov H.S. (average) Cov F.S. (average)
#> 2.680894 408.052454
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> 10.723574 5.361787
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> 836.602526 418.301263
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 2.844451 2.203303 4.926734
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 4.022662 3.115940 6.967454
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 5.740335 4.446445 9.942552
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 8.118060 6.288222 14.060892# Similarly we analyze the line tester data containing only crosses laid out in Alpha lattice design.
# Load the package
library(gpbStat)
# Loading dataset
data("alphaltc")
# Viewing the Structure of dataset
str(alphaltc)
#> 'data.frame': 60 obs. of 5 variables:
#> $ replication: chr "r1" "r1" "r1" "r1" ...
#> $ block : chr "b1" "b1" "b1" "b2" ...
#> $ line : int 5 1 4 4 1 2 2 5 3 1 ...
#> $ tester : int 7 8 8 6 7 7 6 6 8 6 ...
#> $ yield : num 47.3 109.4 36.3 36.2 70.7 ...
# There are five columns replication, block, line, tester and yield.
## Now by using function ltc we analyze the data.
## The first parameter of `ltc` function is "data" followed by replication, line, tester, dependent variable(yield) and block.
## Note: The "block" parameter comes at the end.
results2 = ltc(alphaltc, replication, line, tester, yield, block)
#>
#> Analysis of Line x Tester: yield
## Viewing the results
results2
#> $Means
#> Testers
#> Lines 6 7 8
#> 1 86.47500 88.95833 89.55000
#> 2 88.64667 55.48000 50.12667
#> 3 51.19917 53.28417 36.91583
#> 4 33.47500 34.29833 50.78417
#> 5 45.30417 42.14500 49.98000
#>
#> $`Overall ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 1586.4934 528.8311 3.1440495 4.213104e-02
#> Crosses 14 23862.0199 1704.4300 10.1333150 3.161969e-07
#> Blocks within Replication 16 2555.9198 159.7450 0.9497288 5.307851e-01
#> Lines 4 18835.3119 4708.8280 24.8833344 6.536498e-11
#> Testers 2 463.1458 231.5729 1.2237239 3.037332e-01
#> Lines X Testers 8 4563.5622 570.4453 3.0144615 8.508293e-03
#> Error 26 4373.2165 168.2006 NA NA
#> Total 59 2561.2067 NA NA NA
#>
#> $`Coefficient of Variation`
#> [1] 22.70992
#>
#> $`Genetic Variance`
#> Genotypic Variance Phenotypic Variance Environmental Variance
#> 293.8997 462.1004 168.2006
#>
#> $`Genetic Variability `
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> 37.6417608 30.0193557
#> Environmental coefficient of Variation <NA>
#> 22.7099195 0.6360084
#>
#> $`Line x Tester ANOVA`
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Lines 4 18835.3119 4708.8280 24.883334 6.536498e-11
#> Testers 2 463.1458 231.5729 1.223724 3.037332e-01
#> Lines X Testers 8 4563.5622 570.4453 3.014461 8.508293e-03
#> Error 26 4373.2165 168.2006 NA NA
#>
#> $`GCA lines`
#> 1 2 3 4 5
#> 31.220 7.643 -9.975 -17.589 -11.298
#>
#> $`GCA testers`
#> 6 7 8
#> 3.912 -2.275 -1.637
#>
#> $`SCA crosses`
#> Testers
#> Lines 6 7 8
#> 1 -5.765 2.906 2.859
#> 2 19.984 -6.996 -12.988
#> 3 0.154 8.426 -8.580
#> 4 -9.956 -2.946 12.902
#> 5 -4.417 -1.390 5.807
#>
#> $`Proportional Contribution`
#> Lines Tester Line x Tester
#> 78.934273 1.940933 19.124794
#>
#> $`GV Singh & Chaudhary`
#> Cov H.S. (line) Cov H.S. (tester)
#> 344.86523 -16.94362
#> Cov H.S. (average) Cov F.S. (average)
#> 30.06778 262.35565
#> F = 0, Adittive genetic variance F = 1, Adittive genetic variance
#> 120.27111 60.13555
#> F = 0, Variance due to Dominance F = 1, Variance due to Dominance
#> 201.12232 15.84306
#>
#> $`Standard Errors`
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> 3.743891 2.900005 6.484609
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> 5.294661 4.101227 9.170622
#>
#> $`Critical differance`
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> 7.695678 5.961047 13.329305
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> 10.883332 8.430193 18.850484# Line x Tester analysis for multiple traits laid in Alpha lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data("alphaltcmt")
# View the structure of dataframe.
str(alphaltcmt)
#> Classes 'tbl_df', 'tbl' and 'data.frame': 60 obs. of 7 variables:
#> $ replication: num 1 1 1 1 1 1 1 1 1 1 ...
#> $ block : num 1 1 1 2 2 2 3 3 3 4 ...
#> $ line : chr "l5" "l1" "l2" "l2" ...
#> $ tester : chr "t1" "t3" "t3" "t1" ...
#> $ hsw : num 26.7 22.1 26.2 25.7 18 ...
#> $ sh : num 82.2 83.6 83.8 81.7 81.6 ...
#> $ gy : num 61.3 30.7 48.1 25.9 29.1 ...
# Conduct Line x Tester analysis
result3 = ltcmt(alphaltcmt, replication, line, tester, alphaltcmt[,5:7], block)
#>
#> Analysis of Line x Tester for Multiple traits
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
# View the output
result3
#> $Mean
#> $Mean$hsw
#> Tester
#> Line 1 2 3
#> 1 24.28100 24.38975 26.43250
#> 2 24.75150 23.17850 23.85100
#> 3 22.12950 25.09375 25.46600
#> 4 25.36125 26.52300 26.32225
#> 5 24.40525 23.86375 22.90450
#>
#> $Mean$sh
#> Tester
#> Line 1 2 3
#> 1 82.93436 83.87124 84.20399
#> 2 83.89508 84.62547 83.77366
#> 3 83.61044 84.45869 83.04424
#> 4 84.27547 84.32636 81.81483
#> 5 83.04301 82.58873 84.83067
#>
#> $Mean$gy
#> Tester
#> Line 1 2 3
#> 1 54.26683 48.86251 44.75305
#> 2 44.95867 45.31223 47.39452
#> 3 46.06275 54.77228 55.05693
#> 4 60.56487 52.13965 53.79695
#> 5 58.26799 53.53054 53.55139
#>
#>
#> $ANOVA
#> $ANOVA$hsw
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 123.547315 41.182438 5.2008347 0.006007617
#> Blocks within Replication 16 159.485732 9.967858 1.2588177 0.292524662
#> Crosses 14 95.615586 6.829685 0.8625051 0.603263868
#> Lines 4 44.431866 11.107966 1.0223891 0.406049177
#> Testers 2 6.558666 3.279333 0.3018333 0.740946613
#> Lines X Testers 8 44.625055 5.578132 0.5134172 0.839950285
#> Error 26 205.879143 7.918429 NA NA
#> Total 59 584.527775 NA NA NA
#>
#> $ANOVA$sh
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 47.865214 15.9550714 5.5805022 0.004306487
#> Blocks within Replication 16 61.859599 3.8662250 1.3522645 0.240056532
#> Crosses 14 40.010784 2.8579131 0.9995938 0.481506718
#> Lines 4 3.066186 0.7665466 0.1874088 0.943757507
#> Testers 2 2.486129 1.2430645 0.3039100 0.739429879
#> Lines X Testers 8 34.458468 4.3073085 1.0530702 0.412196780
#> Error 26 74.335936 2.8590745 NA NA
#> Total 59 224.071534 NA NA NA
#>
#> $ANOVA$gy
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 3170.89296 1056.96432 7.6637547 0.0007890292
#> Blocks within Replication 16 2338.16012 146.13501 1.0595843 0.4350901435
#> Crosses 14 1411.76346 100.84025 0.7311646 0.7260111510
#> Lines 4 787.68515 196.92129 0.9743323 0.4310135285
#> Testers 2 48.50139 24.25070 0.1199882 0.8872136703
#> Lines X Testers 8 575.57692 71.94711 0.3559818 0.9379857942
#> Error 26 3585.84969 137.91730 NA NA
#> Total 59 10506.66623 NA NA NA
#>
#>
#> $GCA.Line
#> Trait 1 Trait 2 Trait 3
#> Line 1 0.4375167 -0.01655394 -2.258613
#> Line 2 -0.6699000 0.41165231 -5.664270
#> Line 3 -0.3671500 0.01804113 0.411244
#> Line 4 1.4719333 -0.21419481 3.947743
#> Line 5 -0.8724000 -0.19894469 3.563895
#>
#> $GCA.Tester
#> Trait 1 Trait 2 Trait 3
#> Tester 1 -0.41120 -0.1347434 1.2714786
#> Tester 2 0.01285 0.2876815 -0.6293023
#> Tester 3 0.39835 -0.1529380 -0.6421764
#>
#> $SCA
#> $SCA$`Trait 1`
#> Tester
#> Line 1 2 3
#> 1 -0.3422167 -0.6575167 0.9997333
#> 2 1.2357000 -0.7613500 -0.4743500
#> 3 -1.6890500 0.8511500 0.8379000
#> 4 -0.2963833 0.4413167 -0.1449333
#> 5 1.0919500 0.1264000 -1.2183500
#>
#> $SCA$`Trait 2`
#> Tester
#> Line 1 2 3
#> 1 -0.60075619 -0.08630744 0.6870636
#> 2 -0.06824822 0.23971724 -0.1714690
#> 3 0.04072451 0.46655392 -0.5072784
#> 4 0.93799581 0.56645558 -1.5044514
#> 5 -0.30971591 -1.18641930 1.4961352
#>
#> $SCA$`Trait 3`
#> Tester
#> Line 1 2 3
#> 1 3.701222 0.19768507 -3.8989074
#> 2 -2.201279 0.05305477 2.1482244
#> 3 -7.172713 3.43759274 3.7351205
#> 4 3.792902 -2.73153863 -1.0613638
#> 5 1.879868 -0.95679396 -0.9230737
#>
#>
#> $CV
#> Trait1 Trait2 Trait3
#> 11.440345 2.020495 22.780202
#>
#> $Genetic.Variance.Covariance.
#> Phenotypic Variance Genotypic Variance Environmental Variance
#> Trait 1 -0.6697598 -8.588188 7.918429
#> Trait 2 -0.4152151 -3.274290 2.859074
#> Trait 3 -101.1137222 -239.031018 137.917296
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> Trait 1 NaN NaN
#> Trait 2 NaN NaN
#> Trait 3 NaN NaN
#> Environmental coefficient of Variation Broad sense heritability
#> Trait 1 11.440345 12.822788
#> Trait 2 2.020495 7.885767
#> Trait 3 22.780202 2.363982
#>
#> $Std.Error
#> S.E. gca for line S.E. gca for tester S.E. sca effect
#> Trait 1 0.8123232 0.6292229 1.4069851
#> Trait 2 0.4881150 0.3780922 0.8454399
#> Trait 3 3.3901487 2.6259979 5.8719097
#> S.E. (gi - gj)line S.E. (gi - gj)tester S.E. (sij - skl)tester
#> Trait 1 1.1487985 0.8898555 1.989777
#> Trait 2 0.6902988 0.5347031 1.195633
#> Trait 3 4.7943942 3.7137218 8.304134
#>
#> $C.D.
#> C.D. gca for line C.D. gca for tester C.D. sca effect
#> Trait 1 1.669754 1.2933861 2.892099
#> Trait 2 1.003335 0.7771797 1.737827
#> Trait 3 6.968550 5.3978159 12.069883
#> C.D. (gi - gj)line C.D. (gi - gj)tester C.D. (sij - skl)tester
#> Trait 1 2.361389 1.829124 4.090046
#> Trait 2 1.418929 1.099098 2.457658
#> Trait 3 9.855018 7.633664 17.069393
#>
#> $Add.Dom.Var
#> Cov H.S. (line) Cov H.S. (tester) Cov H.S. (average) Cov F.S. (average)
#> Trait 1 0.4608195 -0.1149399 0.03318511 -0.3379446
#> Trait 2 -0.2950635 -0.1532122 -0.03843094 -0.1627380
#> Trait 3 10.4145144 -2.3848209 0.76610579 -10.5634695
#> Addittive Variance(F=0) Addittive Variance(F=1) Dominance Variance(F=0)
#> Trait 1 0.1327405 0.06637023 -1.170148
#> Trait 2 -0.1537238 -0.07686188 0.724117
#> Trait 3 3.0644232 1.53221158 -32.985091
#> Dominance Variance(F=1)
#> Trait 1 -0.5850742
#> Trait 2 0.3620585
#> Trait 3 -16.4925453
#>
#> $Contribution.of.Line.Tester
#> Lines Tester Line x Tester
#> Trait 1 46.46927 6.859411 46.67132
#> Trait 2 7.66340 6.213647 86.12295
#> Trait 3 55.79441 3.435518 40.77007